Evaluation of Quantified Statements using Gradual Numbers - 64

Dr. Ludovic Liétard is currently assistant professor at the University of Rennes 1 (IUT Lannion) in France. His research mainly concerns flexible querying of relational databases using fuzzy set theory and various applications of fuzzy set theory in databases. Dr. Daniel Rocacher is currently assistant professor at the University of Rennes 1 (ENSSAT Lannion) in France. He has proposed new directions to define gradual numbers in the framework of fuzzy set theory. His current research concerns their applications in databases. Evaluation of Quantified Statements using Gradual Numbers -2 -Abstract. This paper is devoted to the evaluation of quantified statements which can be found in many applications as decision-making, expert systems or flexible querying of relational databases using fuzzy set theory. Its contribution is to introduce the main techniques to evaluate such statements and to propose a new theoretical background for the evaluation of quantified statements of type "Q X are A" and "Q B X are A". In this context, quantified statements are interpreted using an arithmetic on gradual numbers from ℕ f , ℤ f and ℚ f . It is shown that the context of fuzzy numbers provides a framework to unify previous approaches and can be the base for the definition of new approaches

Geometrical Theory of Analytic Functions

The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria